function Uout = multi(Uin,np,emax,fieldeps,fieldom,jx,jz,E0)
    

%        multiplication step in the Chebychev reccursion
        
  
        Uout = hamil(Uin,np,fieldeps,fieldom,jx,jz,E0);

%        normalization of the Hamiltonian operator range
%        from -1 to 1 :
%        H' =  ( 2 H - DE ) /DE 

        Uout = 2*Uout/emax - Uin ;
       end